Researchers map phase boundary of complex contagion with SIS recovery

Complex contagion—where adoption requires reinforcement from multiple neighbors—has been well-studied in monotone (no-recovery) settings, but its phase diagram under SIS-like recovery remained unmapped. In their paper "Phase Boundary of a Stochastic Watts-Threshold SIS Model on Random Networks," researchers Yasmine Beji, Heger Arfaoui, and Slimane BenMiled close this gap. They analyze a stochastic Watts-threshold SIS model on both Erdos-Renyi and Barabasi-Albert random networks, reconstructing the extinction-persistence phase boundary across three key parameters: transmission rate β, adoption threshold θ, and infectious duration d.

Using adaptive Delaunay-based sampling and weighted logistic regression on over 180,000 Monte Carlo trials, they uncover three main findings. First, the phase boundary is accurately described by a six-parameter interaction model whose structure remains invariant across both network topologies. Second, the transition between extinction and persistence is remarkably sharp: the 10–90% extinction-probability band spans only Δθ ≈ 0.005–0.008. Third, the adoption threshold θ is the dominant parameter governing epidemic feasibility, while transmission rate and infectious duration play secondary, asymmetric roles. This work provides the first quantitative reference for the complex-contagion analogue of the classical SIS epidemic threshold.